Maximum eccentric connectivity index for graphs with given diameter

Hauweele, Pierre
University of Mons, Belgium

Hertz, Alain
Ecole Polytechnique de Montréal, Canada

Mélot, Hadrien
University of Mons, Belgium

Ries, Bernard
University of Fribourg, Switzerland

Devillez, Gauvain
University of Mons, Belgium
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Published in:
 Discrete Applied Mathematics.  2019, vol. 268, p. 102111
English
The eccentricity of a vertex v in a graph G is the maximum distance between v and any other vertex of G. The diameter of a graph G is the maximum eccentricity of a vertex in G. The eccentric connectivity index of a connected graph is the sum over all vertices of the product between eccentricity and degree. Given two integers n and D with D ≤ n−1, we characterize those graphs which have the largest eccentric connectivity index among all connected graphs of order n and diameter D. As a corollary, we also characterize those graphs which have the largest eccentric connectivity index among all connected graphs of a given order n.

Faculty
 Faculté des sciences économiques et sociales et du management

Department
 Département d'informatique

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Computer science

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https://folia.unifr.ch/unifr/documents/308059
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